Star Trek: 10 Things You Didn't Know About The Kobayashi Maru

In canon, it is not known if the Kobayashi Maru — that is to say, the Class III neutronic fuel carrier that bears the name — ever existed outside of the simulation. In fact, the Kobayashi Maru is never actually seen in The Wrath of Khan. Its counterpart is all but virtually absent from Star Trek (2009), save for a couple of screenshots. That version did get its own Eaglemoss model — the ECS-1022. The Kobayashi Maru from Star Trek: Prodigy's Kobayashi had a different design still, with an NCC registry. 

The reference work Star Trek: Star Charts gives the real "S.S. Kobayashi Maru" as "Lost (2245)" just outside of Klingon space. The catch there, aside from blurry non-officialdom, is that the date is (now) awfully close to Kirk's start at the Academy —2252 by all accounts. It seems a bit inconsiderate to base a test for teenagers on the loss of a very real ship in the first place. Leaving only about seven year's distance to the actual event is practically dancing on graves.

If hindsight helps, the Star Trek: Enterprise novel Kobayashi Maru dates the loss of the titular vessel that inspired the simulation as much earlier, in 2155. The situation is largely similar to the parameters of the test — gravitic mine in the Gamma Hydra system — but in this case, the Romulans are involved.